Fuzion • Idioms • Idiom # 204: Return fraction and exponent of a real number

Idiom # 204: Return fraction and exponent of a real number

Code

bits := f.cast_to_u64
fract_bits := f64.significand_bits.as_u64 - 1
bias := (u64 2 ** (f64.exponent_bits.as_u64 - 1) - 1)
mask := u64 2 ** f64.exponent_bits.as_u64 - 1
e := ((bits >> fract_bits) & mask).as_i32 - bias.as_i32 + 1
bits2 := bits & (~(mask << fract_bits))
bits3 := bits2 | ((bias - 1) << fract_bits)
if ((bits >> fract_bits) & mask) = 0 then
  (bits3.cast_to_f64, e - 51)
else
  (bits3.cast_to_f64, e)

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bits := f.cast_to_u64
fract_bits := f64.significand_bits.as_u64 - 1
bias := (u64 2 ** (f64.exponent_bits.as_u64 - 1) - 1)
mask := u64 2 ** f64.exponent_bits.as_u64 - 1
e := ((bits >> fract_bits) & mask).as_i32 - bias.as_i32 + 1
bits2 := bits & (~(mask << fract_bits))
bits3 := bits2 | ((bias - 1) << fract_bits)
if ((bits >> fract_bits) & mask) = 0 then
  (bits3.cast_to_f64, e - 51)
else
  (bits3.cast_to_f64, e)
 
 
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What are effects?

Runnable Example

ex204 is
  frexp (f f64) tuple f64 i32 =>
    bits := f.cast_to_u64
    # bits is f in the following representation
    # seeeeeeeeeeeffffffffffffffffffffffffffffffffffffffffffffffffffff
    # where s = sign, e = exponent, f = fraction
    fract_bits := f64.significand_bits.as_u64 - 1
    # fract_bits is
    # 0000000000000000000000000000000000000000000000000000000000110100
    bias := (u64 2 ** (f64.exponent_bits.as_u64 - 1) - 1)
    # bias is
    # 0000000000000000000000000000000000000000000000000000001111111111
    mask := u64 2 ** f64.exponent_bits.as_u64 - 1
    # mask is
    # 0000000000000000000000000000000000000000000000000000011111111111
    # bits >> fract_bits will give us
    # 0000000000000000000000000000000000000000000000000000seeeeeeeeeee
    # AND this with mask
    # 00000000000000000000000000000000000000000000000000000eeeeeeeeeee
    e := ((bits >> fract_bits) & mask).as_i32 - bias.as_i32 + 1
    # mask << fract_bits is
    # 0111111111110000000000000000000000000000000000000000000000000000
    # NOT this to get
    # 1000000000001111111111111111111111111111111111111111111111111111
    bits2 := bits & (~(mask << fract_bits))
    # hence bits2 is
    # s00000000000ffffffffffffffffffffffffffffffffffffffffffffffffffff
    # (bias - 1) << fract_bits is
    # 0011111111100000000000000000000000000000000000000000000000000000
    bits3 := bits2 | ((bias - 1) << fract_bits)
    # therefore we have
    # s01111111110ffffffffffffffffffffffffffffffffffffffffffffffffffff
    # the last step is to "normalize" the exponent of the fraction
    if ((bits >> fract_bits) & mask) = 0 then
      (bits3.cast_to_f64, e - 51)
    else
      (bits3.cast_to_f64, e)

  a f64 := 3.14
  (b, c) := frexp a
  say "{b} {c}"

  d f64 := 5E-324
  (exp, fract) := frexp d
  say "{exp} {fract}"

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ex204 is
  frexp (f f64) tuple f64 i32 =>
    bits := f.cast_to_u64
    # bits is f in the following representation
    # seeeeeeeeeeeffffffffffffffffffffffffffffffffffffffffffffffffffff
    # where s = sign, e = exponent, f = fraction
    fract_bits := f64.significand_bits.as_u64 - 1
    # fract_bits is
    # 0000000000000000000000000000000000000000000000000000000000110100
    bias := (u64 2 ** (f64.exponent_bits.as_u64 - 1) - 1)
    # bias is
    # 0000000000000000000000000000000000000000000000000000001111111111
    mask := u64 2 ** f64.exponent_bits.as_u64 - 1
    # mask is
    # 0000000000000000000000000000000000000000000000000000011111111111
    # bits >> fract_bits will give us
    # 0000000000000000000000000000000000000000000000000000seeeeeeeeeee
    # AND this with mask
    # 00000000000000000000000000000000000000000000000000000eeeeeeeeeee
    e := ((bits >> fract_bits) & mask).as_i32 - bias.as_i32 + 1
    # mask << fract_bits is
    # 0111111111110000000000000000000000000000000000000000000000000000
    # NOT this to get
    # 1000000000001111111111111111111111111111111111111111111111111111
    bits2 := bits & (~(mask << fract_bits))
    # hence bits2 is
    # s00000000000ffffffffffffffffffffffffffffffffffffffffffffffffffff
    # (bias - 1) << fract_bits is
    # 0011111111100000000000000000000000000000000000000000000000000000
    bits3 := bits2 | ((bias - 1) << fract_bits)
    # therefore we have
    # s01111111110ffffffffffffffffffffffffffffffffffffffffffffffffffff
    # the last step is to "normalize" the exponent of the fraction
    if ((bits >> fract_bits) & mask) = 0 then
      (bits3.cast_to_f64, e - 51)
    else
      (bits3.cast_to_f64, e)
  a f64 := 3.14
  (b, c) := frexp a
  say "{b} {c}"
  d f64 := 5E-324
  (exp, fract) := frexp d
  say "{exp} {fract}"
 
 
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What are effects?

last changed: 2024-07-01

next: Idiom # 205: Get an environment variable